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2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft 2) above the ground. At what rate is the length of his shadow changing when he is 6 ft from the base of the pole that supports the light? Enter just an integer (no units). the problem. 3) Given the revenue and cost functions R(x) = 34x-0.7x2 and C(x) = 3x + 13, where x is the daily production, find the rate of change of profit with respect to time when x = 15 units and dx dt --4 units per day. A) $103/day B) $118.4/day C) $40/day D) $52/day 4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 3 m²/sec, how fast are the people moving when they are 3 m from the right angle? (Round approximations to two decimal places.) A) 3.00 m/sec B) 2.00 m/sec C) 0.50 m/sec D) 1.00 m/sec

2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft 2) above the ground. At what rate is the length of his shadow changing when he is 6 ft from the base of the pole that supports the light? Enter just an integer (no units). the problem. 3) Given the revenue and cost functions R(x) = 34x-0.7x2 and C(x) = 3x + 13, where x is the daily production, find the rate of change of profit with respect to time when x = 15 units and dx dt --4 units per day. A) $103/day B) $118.4/day C) $40/day D) $52/day 4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 3 m²/sec, how fast are the people moving when they are 3 m from the right angle? (Round approximations to two decimal places.) A) 3.00 m/sec B) 2.00 m/sec C) 0.50 m/sec D) 1.00 m/sec

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1) 1) The radius of a spherical balloon increases at a rate of 1 mm/sec. How fast is the surface area increasing when the radius is 10mm? (Note: The surface area S of a sphere of radius r is S = 47tr2.) Enter just a real number (no approximations, no units or words). 2) 2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft above the ground. At what rate is the length of his shadow changing when he is 6 ft from the base of the pole that supports the light? Enter just an integer (no units). Solve the problem. 3) Given the revenue and cost functions R(x) = 34x - 0.7x2 and C(x) = 3x + 13, where x is the daily production, find the rate of change of profit with respect to time when x = 15 units and dx = 4 units per day. dt C) $40/day D) $52/day 4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 3 m²/sec, how fast are the people moving when they are 3 m from the right angle? (Round A) $103/day approximations to two decimal places.) A) 3.00 m/sec B) 2.00 m/sec B) $118.4/day C) 0.50 m/sec 5) A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping at the constant rate of 4 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 5 ft from the wall? A) 9.6 ft/s B) 10.4 ft/s C) 2.4 ft/s D) 0.80 ft/s Solve the problem. Round your answer, if appropriate. 6) One airplane is approaching an airport from the north at 151 km/hr. A second airplane approaches from the east at 203 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 26 km away from the airport and the westbound plane is 15 km from the airport. A) -232 km/hr B)-116 km/hr C) -464 km/hr D) -348 km/hr D) 1.00 m/sec 7) The radius of a right circular cylinder is increasing at the rate of 10 in./sec, while the height is decreasing at the rate of 5 in./sec. At what rate is the volume of the cylinder changing when the radius is 6 in. and the height is 12 in.? D) 540 in.3/sec A) 12607 in.3/sec B) 540 in.3/sec C) -210 in.3/sec A) 8) The volume of a sphere is increasing at a rate of 2 cm³/sec. Find the rate of change of its surface area when its volume is 2567 cm3. (Do not round your answer.) 3 cm²/sec B) cm²/sec C) 47 cm²/sec 3 D) 1 cm2/sec 9) Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 3.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 3.00 inches deep, the surface level is falling at a rate of 1.7 in./sec. Find the rate at which water is being drained from the container. A) 22.4 in.3s B) 25.0 in.3/s C) 17.3 in.3/s D) 16.5 in.3/s C) c) ft/sec 2 10) A man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 18 ft high. At what rate is the length of his shadow changing when he is 30 ft away from the lamppost? (Do not round your answer) A) 3 ft/sec B) ft/sec D) 30 ft/sec 3) 4) 5) 6) 7) 8) 9) 10)
Transcribed Image Text:1) 1) The radius of a spherical balloon increases at a rate of 1 mm/sec. How fast is the surface area increasing when the radius is 10mm? (Note: The surface area S of a sphere of radius r is S = 47tr2.) Enter just a real number (no approximations, no units or words). 2) 2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft above the ground. At what rate is the length of his shadow changing when he is 6 ft from the base of the pole that supports the light? Enter just an integer (no units). Solve the problem. 3) Given the revenue and cost functions R(x) = 34x - 0.7x2 and C(x) = 3x + 13, where x is the daily production, find the rate of change of profit with respect to time when x = 15 units and dx = 4 units per day. dt C) $40/day D) $52/day 4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 3 m²/sec, how fast are the people moving when they are 3 m from the right angle? (Round A) $103/day approximations to two decimal places.) A) 3.00 m/sec B) 2.00 m/sec B) $118.4/day C) 0.50 m/sec 5) A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping at the constant rate of 4 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 5 ft from the wall? A) 9.6 ft/s B) 10.4 ft/s C) 2.4 ft/s D) 0.80 ft/s Solve the problem. Round your answer, if appropriate. 6) One airplane is approaching an airport from the north at 151 km/hr. A second airplane approaches from the east at 203 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 26 km away from the airport and the westbound plane is 15 km from the airport. A) -232 km/hr B)-116 km/hr C) -464 km/hr D) -348 km/hr D) 1.00 m/sec 7) The radius of a right circular cylinder is increasing at the rate of 10 in./sec, while the height is decreasing at the rate of 5 in./sec. At what rate is the volume of the cylinder changing when the radius is 6 in. and the height is 12 in.? D) 540 in.3/sec A) 12607 in.3/sec B) 540 in.3/sec C) -210 in.3/sec A) 8) The volume of a sphere is increasing at a rate of 2 cm³/sec. Find the rate of change of its surface area when its volume is 2567 cm3. (Do not round your answer.) 3 cm²/sec B) cm²/sec C) 47 cm²/sec 3 D) 1 cm2/sec 9) Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 3.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 3.00 inches deep, the surface level is falling at a rate of 1.7 in./sec. Find the rate at which water is being drained from the container. A) 22.4 in.3s B) 25.0 in.3/s C) 17.3 in.3/s D) 16.5 in.3/s C) c) ft/sec 2 10) A man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 18 ft high. At what rate is the length of his shadow changing when he is 30 ft away from the lamppost? (Do not round your answer) A) 3 ft/sec B) ft/sec D) 30 ft/sec 3) 4) 5) 6) 7) 8) 9) 10)
Expert Solution
Introduction

As per the question we will only solve the subparts (2), (3), (4)

 

(2) In this problem, we are given the height and walking speed of a person who is walking towards a street light, and we are asked to find the rate of change of the length of their shadow when they are a certain distance away from the base of the pole that supports the light.

 

(3) This problem involves revenue and cost functions for a daily production process, and we are asked to find the rate of change of profit with respect to time when the production level and the rate of change of production are both given.

 

(4) As per the question, two people are walking at the same speed along different legs of a right triangle-shaped piece of land, and we are given the rate of change of the area of the land. We are asked to find the rate at which the people are moving when they are a certain distance away from the right angle of the triangle.

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